The common stock of the C.A.L.L. Corporation has been trading in a narrow range

Question

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $95 per share for months, and you believe it is going to stay in that range for the next 3 months. The price of a 3-month put option with an exercise price of $95 is $6.00. a. If the risk-free interest rate is 9% per year, what must be the price of a 3-month call option on C.A.L.L. stock at an exercise price of $95 if it is at the money? (The stock pays no dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of a 3-month call option b-1. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price's future movement? Strategy

Explanation / Answer

Put call parity states that
S+P=C+Xe^(-rt)
1
=>C=S+P-Xe^(-rt)
=>C=95+6-95*e^(-9%*3/12)=8.113632

2
Sell 95 strike call and sell 2puts of 95 strike

3
Profit=-max(S-95,0)-2*max(95-S,0)+6*2+8.113632
Stock<80 Profit=-170+2S+0.113632=2S-169.886
Stock>95 Profit=-S+95+6*2+8.113632=-S+115.113632

Maximum Profit=-90+115.113632=20.113632

4
If stock price falls below 169.886/2=84.943 and rises more than 115.113632, we will start losing money

5
S=C+Xe^(-rt)-P
Long Call
Sell Put
Lend present value of strike
Cost=8.113632+95e^(-3%*9/12)-6=95

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